{"fg_target": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x; you alone: 2.84x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x; you alone: 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x; you alone: 0.48x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x; you alone: 1.24x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x; you alone: est. 0.76x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}}, "frontier_gated": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x; you alone: 2.84x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x; you alone: 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x; you alone: 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x; you alone: 0.48x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x; you alone: 1.24x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x; you alone: est. 0.76x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x; you alone: 0.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 1.39x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 1.39x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nOnly items that beat your own typical result on the problem they were verified on are kept, plus environment and correctness facts. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}}, "lessons_only": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel."}}, "no_approach": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}}, "no_numbers": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (verified by the protected evaluator)\n- [verified on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (verified by the protected evaluator)\n- [verified on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [verified on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (verified by the protected evaluator)\n- [verified on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [verified on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [verified on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [verified on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [verified on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (verified by the protected evaluator)\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [verified on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [verified on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [verified on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [verified on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (verified by the protected evaluator)\n- [verified on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small. For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (verified by the protected evaluator)\n- [verified on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still slower than cuBLAS. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (verified by the protected evaluator)\n- [verified on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [verified on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [verified on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [verified on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [verified on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [verified on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}}, "no_prohib": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns."}}, "none": {"claude-opus-4-8": {"L1_008": "", "L1_012": "", "L1_050": "", "L1_056": "", "L1_058": "", "L1_061": "", "L1_062": "", "L1_065": "", "L1_066": "", "L1_071": "", "L1_072": "", "L1_077": "", "L1_078": "", "L1_080": "", "L1_083": "", "L1_085": "", "L2_006": "", "L2_008": "", "L2_011": "", "L2_014": "", "L2_018": "", "L2_022": "", "L2_024": "", "L2_025": "", "L2_027": "", "L2_028": "", "L2_029": "", "L2_030": "", "L2_033": "", "L2_035": "", "L2_039": "", "L2_041": "", "L2_043": "", "L2_046": "", "L2_047": "", "L2_048": "", "L2_050": "", "L2_052": "", "L2_057": "", "L2_061": "", "L2_067": "", "L2_069": "", "L2_071": "", "L2_073": "", "L2_074": "", "L2_075": "", "L2_076": "", "L2_077": "", "L2_079": "", "L2_082": "", "L2_085": "", "L2_086": "", "L2_089": "", "L2_092": "", "L2_094": "", "L3_004": "", "L3_008": "", "L3_009": "", "L3_010": "", "L3_014": "", "L3_020": "", "L3_021": "", "L3_023": "", "L3_024": "", "L3_030": "", "L3_032": "", "L3_036": "", "L3_037": "", "L3_038": "", "L3_039": "", "L3_040": "", "L3_041": "", "L3_042": "", "L3_046": "", "L3_049": ""}, "claude-opus-5-5": {"L1_008": "", "L1_012": "", "L1_050": "", "L1_056": "", "L1_058": "", "L1_061": "", "L1_062": "", "L1_065": "", "L1_066": "", "L1_071": "", "L1_072": "", "L1_077": "", "L1_078": "", "L1_080": "", "L1_083": "", "L1_085": "", "L2_006": "", "L2_008": "", "L2_011": "", "L2_014": "", "L2_018": "", "L2_022": "", "L2_024": "", "L2_025": "", "L2_027": "", "L2_028": "", "L2_029": "", "L2_030": "", "L2_033": "", "L2_035": "", "L2_039": "", "L2_041": "", "L2_043": "", "L2_046": "", "L2_047": "", "L2_048": "", "L2_050": "", "L2_052": "", "L2_057": "", "L2_061": "", "L2_067": "", "L2_069": "", "L2_071": "", "L2_073": "", "L2_074": "", "L2_075": "", "L2_076": "", "L2_077": "", "L2_079": "", "L2_082": "", "L2_085": "", "L2_086": "", "L2_089": "", "L2_092": "", "L2_094": "", "L3_004": "", "L3_008": "", "L3_009": "", "L3_010": "", "L3_014": "", "L3_020": "", "L3_021": "", "L3_023": "", "L3_024": "", "L3_030": "", "L3_032": "", "L3_036": "", "L3_037": "", "L3_038": "", "L3_039": "", "L3_040": "", "L3_041": "", "L3_042": "", "L3_046": "", "L3_049": ""}}, "prior": {"claude-opus-4-8": {"L1_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_012": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_050": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_056": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_058": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_061": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_062": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_065": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_066": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_071": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_072": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_077": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_078": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_080": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_083": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_085": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_006": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_011": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_014": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_018": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_022": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_024": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_025": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_027": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_028": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_029": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_030": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_033": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_035": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_039": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_041": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_043": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_046": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_047": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_048": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_050": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_052": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_057": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_061": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_067": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_069": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_071": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_073": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_074": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_075": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_076": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_077": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_079": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_082": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_085": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_086": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_089": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_092": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_094": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_004": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_009": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_010": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_014": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_020": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_021": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_023": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_024": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_030": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_032": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_036": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_037": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_038": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_039": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_040": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_041": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_042": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_046": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_049": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete."}, "claude-opus-5-5": {"L1_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_012": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_050": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_056": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_058": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_061": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_062": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_065": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_066": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_071": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_072": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_077": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_078": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_080": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_083": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L1_085": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_006": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_011": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_014": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_018": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_022": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_024": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_025": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_027": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_028": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_029": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_030": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_033": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_035": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_039": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_041": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_043": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_046": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_047": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_048": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_050": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_052": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_057": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_061": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_067": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_069": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_071": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_073": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_074": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_075": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_076": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_077": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_079": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_082": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_085": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_086": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_089": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_092": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L2_094": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_004": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_008": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_009": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_010": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_014": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_020": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_021": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_023": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_024": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_030": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_032": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_036": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_037": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_038": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_039": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_040": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_041": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_042": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_046": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete.", "L3_049": "Working principles (general, not specific to any task): be thorough and verify against the live environment state. When a tool or API returns an empty, missing or surprising result where you expected data, do not take it at face value: investigate before concluding, check the arguments you passed, and try reasonable alternatives. Make sure you have collected all of the information the task needs. Before finishing, re-check that your answer and every required action are correct and complete."}}, "reader_relative": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x; you alone: 2.84x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 0.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: est. 0.14x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.22x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x; you alone: 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x; you alone: 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm; you alone: 10.00x] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x; you alone: 0.64x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 0.47x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x; you alone: 0.48x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x; you alone: 1.08x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x; you alone: 1.24x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 0.65x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x; you alone: est. 0.76x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x; you alone: 0.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 0.76x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 0.53x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 0.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 0.74x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 0.57x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 0.63x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 0.57x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 0.78x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 0.53x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 0.96x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.24x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 0.64x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 0.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 0.99x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: est. 0.14x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 0.00x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 0.98x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 1.45x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 0.51x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 1.16x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 0.25x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 0.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 0.00x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 0.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: est. 0.20x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 3.85x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 2.84x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.01x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.02x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 0.00x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 3.85x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for you (Claude Opus 4.8) on earlier training problems; their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 4.90x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x; you alone: 4.81x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: 3.44x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: 3.44x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: 3.44x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x; you alone: 2.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x; you alone: est. 3.18x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x; you alone: 3.44x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x; you alone: 2.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x; you alone: 0.97x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x; you alone: 2.69x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 3.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x; you alone: 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x; you alone: 1.07x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 1.12x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 1.12x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 1.39x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 2.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm; you alone: 9.96x] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x; you alone: 9.96x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x; you alone: 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 2.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x; you alone: 1.39x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x; you alone: 2.04x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x; you alone: 4.09x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 1.88x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 3.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 1.88x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 3.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x; you alone: 1.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 1.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 2.31x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 2.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 1.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 2.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 1.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x; you alone: 2.31x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 1.12x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x; you alone: 3.50x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x; you alone: est. 4.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x; you alone: 1.24x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max; you alone: est. 4.26x] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x; you alone: 1.78x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x; you alone: 1.12x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp; you alone: est. 2.27x] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x; you alone: 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x; you alone: est. 2.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x; you alone: 1.13x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__; you alone: 2.96x] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool; you alone: 10.00x] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract; you alone: 1.26x] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU; you alone: 1.29x] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max; you alone: 8.86x] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x; you alone: 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x; you alone: 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel; you alone: 2.40x] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max; you alone: 3.50x] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling; you alone: 1.78x] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp; you alone: 2.66x] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x; you alone: 2.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x; you alone: 1.88x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x; you alone: 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x; you alone: est. 2.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet; you alone: 1.21x] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x; you alone: 1.21x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN; you alone: 1.45x] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x; you alone: 1.45x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd; you alone: 10.00x] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices; you alone: 4.90x] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices; you alone: 4.81x] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish; you alone: 1.13x] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum; you alone: 1.07x] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd; you alone: 1.02x] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x; you alone: 10.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x; you alone: 4.90x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### How to read this memory (relative to you)\nThese items were verified for an older, weaker model (Claude Opus 4.8); their speedups are floors, not targets. Next to each recipe and verified kernel is your own mean protected speedup on that same source problem without this memory ('you alone'; 'est.' = your average on similar problems). CUDA C++ (load_inline) and Triton are equally available; that these items are written in Triton says nothing about which is faster here.\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}}, "show_all": {"claude-opus-4-8": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}, "claude-opus-5-5": {"L1_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```", "L1_012": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```\n\n### A verified kernel for a related matmul problem (L1_014 Matmul_for_upper_triangular_matrices, 4.11x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef triu_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    # skip tiles entirely in lower triangle: n_hi < m_lo\n    if (n_lo + BLOCK_N - 1) < m_lo:\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    # k from i to j => k in [m_lo, n_hi]\n    k_start = (m_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(n_lo + BLOCK_N, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] <= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        triu_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L1_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_056": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_058": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_062": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_065": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_066": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_072": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```", "L1_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L1_078 conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__, 2.29x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    oc = t % OC\n    ic = t // OC\n    src = ((ic * OC + oc) * KH + kh) * KW + kw\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((oc * IC + ic) * KH + fkh) * KW + fkw\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: tuple,\n                 stride: tuple = (1, 1), padding: tuple = (0, 0), bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose2d = nn.ConvTranspose2d(in_channels, out_channels, kernel_size,\n                                                   stride=stride, padding=padding, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.kernel_size = kernel_size\n        self.in_channels = in_channels\n        self.out_channels = out_channels\n        self.has_bias = bias\n\n    def forward(self, x):\n        stride_ok = (self.stride == (1, 1) or self.stride == 1)\n        if stride_ok and x.is_cuda:\n            w = self.conv_transpose2d.weight  # (IC, OC, KH, KW)\n            IC, OC, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KH, KW, BLOCK=BLOCK)\n            pad_h = KH - 1 - self.padding[0]\n            pad_w = KW - 1 - self.padding[1]\n            b = self.conv_transpose2d.bias if self.has_bias else None\n            return torch.nn.functional.conv2d(x, wf, bias=b, stride=1,\n                                              padding=(pad_h, pad_w))\n        return self.conv_transpose2d(x)\n```", "L1_078": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L1_061 conv_transposed_3D__square_input__square_kernel, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef flip_kernel(w_ptr, o_ptr, IC, OC, KD, KH, KW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = IC * OC * KD * KH * KW\n    mask = offs < total\n    o = offs\n    kw = o % KW\n    t = o // KW\n    kh = t % KH\n    t = t // KH\n    kd = t % KD\n    t = t // KD\n    oc = t % OC\n    ic = t // OC\n    src = ((((ic * OC + oc) * KD + kd) * KH + kh) * KW + kw)\n    fkd = KD - 1 - kd\n    fkh = KH - 1 - kh\n    fkw = KW - 1 - kw\n    dst = ((((oc * IC + ic) * KD + fkd) * KH + fkh) * KW + fkw)\n    v = tl.load(w_ptr + src, mask=mask, other=0.0)\n    tl.store(o_ptr + dst, v, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, output_padding: int = 0, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv_transpose3d = nn.ConvTranspose3d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size, kernel_size), stride=stride, padding=padding, output_padding=output_padding, groups=groups, bias=bias)\n        self.stride = stride\n        self.padding = padding\n        self.output_padding = output_padding\n        self.groups = groups\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        simple = (self.stride == 1 and self.output_padding == 0 and self.groups == 1 and x.is_cuda)\n        if simple:\n            w = self.conv_transpose3d.weight  # (IC, OC, KD, KH, KW)\n            IC, OC, KD, KH, KW = w.shape\n            wf = torch.empty((OC, IC, KD, KH, KW), device=w.device, dtype=w.dtype)\n            total = IC * OC * KD * KH * KW\n            BLOCK = 256\n            flip_kernel[(triton.cdiv(total, BLOCK),)](\n                w.contiguous(), wf, IC, OC, KD, KH, KW, BLOCK=BLOCK)\n            p = KD - 1 - self.padding\n            b = self.conv_transpose3d.bias if self.has_bias else None\n            return F.conv3d(x, wf, bias=b, stride=1, padding=(p, p, p))\n        return self.conv_transpose3d(x)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```", "L1_080": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```", "L1_083": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_085 conv_depthwise_2D_asymmetric_input_asymmetric_kernel, 1.35x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride_h, stride_w, pad_h, pad_w, dil_h, dil_w,\n                  KH: tl.constexpr, KW: tl.constexpr,\n                  HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw0 = ow * stride_w - pad_w\n    ih0 = oh * stride_h - pad_h\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * (KH * KW)\n\n    for kh in tl.static_range(KH):\n        ih = ih0 + kh * dil_h\n        if (ih >= 0) & (ih < H):\n            rbase = base + ih.to(tl.int64) * W\n            for kw in tl.static_range(KW):\n                iw = iw0 + kw * dil_w\n                wvalid = mask & (iw >= 0) & (iw < W)\n                idx = rbase + iw\n                v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n                wv = tl.load(w_ptr + wbase + kh * KW + kw)\n                acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, out_channels: int, kernel_size_h: int, kernel_size_w: int,\n                 stride_h: int = 1, stride_w: int = 1, padding_h: int = 0, padding_w: int = 0,\n                 dilation_h: int = 1, dilation_w: int = 1, groups: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),\n                                stride=(stride_h, stride_w), padding=(padding_h, padding_w),\n                                dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.KH = kernel_size_h\n        self.KW = kernel_size_w\n        self.stride_h = stride_h\n        self.stride_w = stride_w\n        self.padding_h = padding_h\n        self.padding_w = padding_w\n        self.dilation_h = dilation_h\n        self.dilation_w = dilation_w\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        KH, KW = self.KH, self.KW\n        OH = (H + 2 * self.padding_h - self.dilation_h * (KH - 1) - 1) // self.stride_h + 1\n        OW = (W + 2 * self.padding_w - self.dilation_w * (KW - 1) - 1) // self.stride_w + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 128\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            self.stride_h, self.stride_w, self.padding_h, self.padding_w,\n                            self.dilation_h, self.dilation_w,\n                            KH=KH, KW=KW,\n                            HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L1_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L1_083 conv_depthwise_2D_square_input_asymmetric_kernel, 2.43x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef dwconv_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n                  N, C, H, W, OH, OW,\n                  stride, padding, dilation,\n                  K: tl.constexpr, HAS_BIAS: tl.constexpr, BLOCK: tl.constexpr):\n    pid_row = tl.program_id(0)\n    pid_col = tl.program_id(1)\n\n    oh = pid_row % OH\n    tmp = pid_row // OH\n    c = tmp % C\n    n = tmp // C\n\n    ow = pid_col * BLOCK + tl.arange(0, BLOCK)\n    mask = ow < OW\n\n    iw = ow * stride - padding\n    ih0 = oh * stride - padding\n    wvalid = mask & (iw >= 0) & (iw < W)\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    wbase = c * K\n\n    for k in tl.static_range(K):\n        ih = ih0 + k * dilation\n        if (ih >= 0) & (ih < H):\n            idx = base + ih.to(tl.int64) * W + iw\n            v = tl.load(x_ptr + idx, mask=wvalid, other=0.0)\n            wv = tl.load(w_ptr + wbase + k)\n            acc += v * wv\n\n    if HAS_BIAS:\n        bv = tl.load(b_ptr + c)\n        acc += bv\n\n    obase = ((n.to(tl.int64) * C + c) * OH + oh) * OW\n    tl.store(out_ptr + obase + ow, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, dilation: int = 1, bias: bool = False):\n        super(ModelNew, self).__init__()\n        self.conv2d = nn.Conv2d(in_channels, in_channels, kernel_size=(kernel_size, 1),\n                                stride=stride, padding=padding, dilation=dilation,\n                                groups=in_channels, bias=bias)\n        self.in_channels = in_channels\n        self.kernel_size = kernel_size\n        self.stride = stride\n        self.padding = padding\n        self.dilation = dilation\n        self.has_bias = bias\n\n    def forward(self, x: torch.Tensor) -> torch.Tensor:\n        x = x.contiguous()\n        N, C, H, W = x.shape\n        K = self.kernel_size\n        stride = self.stride\n        padding = self.padding\n        dilation = self.dilation\n        OH = (H + 2 * padding - dilation * (K - 1) - 1) // stride + 1\n        OW = (W + 2 * padding - 1) // stride + 1\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        w = self.conv2d.weight.contiguous().view(-1)\n        if self.has_bias:\n            b = self.conv2d.bias.contiguous()\n        else:\n            b = torch.empty(1, device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        grid = (N * C * OH, triton.cdiv(OW, BLOCK))\n        dwconv_kernel[grid](x, w, b, out,\n                            N, C, H, W, OH, OW,\n                            stride, padding, dilation,\n                            K=K, HAS_BIAS=self.has_bias, BLOCK=BLOCK,\n                            num_warps=4)\n        return out\n```\n\n### A verified kernel for a related conv problem (L1_050 conv_standard_2D__square_input__square_kernel, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_kernel(x_ptr, bias_ptr, N, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    tl.store(x_ptr + offs, v + b, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, num_classes=1000):\n        super(ModelNew, self).__init__()\n        self.conv1 = nn.Conv2d(in_channels=3, out_channels=96, kernel_size=11, stride=4, padding=2)\n\n    def forward(self, x):\n        out = F.conv2d(x, self.conv1.weight, None, stride=4, padding=2)\n        out = out.contiguous()\n        N, C, H, W = out.shape\n        S = H * W\n        TOTAL = N * C * S\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bias_kernel[grid](out, self.conv1.bias.contiguous(), N, C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_006": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_027 Conv3d_HardSwish_GroupNorm_Mean, 1.17x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel(x_ptr, chmean_ptr, gmean_ptr, gvar_ptr,\n                 C, S, G, CPG, eps, BLOCK: tl.constexpr):\n    # one program per (b, group)\n    pid = tl.program_id(0)\n    b = pid // G\n    g = pid % G\n    group_base = (b.to(tl.int64) * C + g * CPG) * S\n    gsum = 0.0\n    gsumsq = 0.0\n    for ci in range(CPG):\n        c = g * CPG + ci\n        base = (b.to(tl.int64) * C + c) * S\n        csum = 0.0\n        for off in range(0, S, BLOCK):\n            idx = off + tl.arange(0, BLOCK)\n            mask = idx < S\n            v = tl.load(x_ptr + base + idx, mask=mask, other=0.0)\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            hsm = tl.where(mask, hs, 0.0)\n            csum += tl.sum(hsm)\n            gsumsq += tl.sum(hsm * hsm)\n        gsum += csum\n        tl.store(chmean_ptr + (b.to(tl.int64) * C + c), csum / S)\n    n = CPG * S\n    mean = gsum / n\n    var = gsumsq / n - mean * mean\n    tl.store(gmean_ptr + pid, mean)\n    tl.store(gvar_ptr + pid, var)\n\n\n@triton.jit\ndef final_kernel(chmean_ptr, gmean_ptr, gvar_ptr, w_ptr, b_ptr, out_ptr,\n                 B, C, G, CPG, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < B * C\n    bidx = offs // C\n    c = offs % C\n    g = c // CPG\n    gidx = bidx * G + g\n    cm = tl.load(chmean_ptr + offs, mask=mask, other=0.0)\n    gm = tl.load(gmean_ptr + gidx, mask=mask, other=0.0)\n    gv = tl.load(gvar_ptr + gidx, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    bb = tl.load(b_ptr + c, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(gv + eps)\n    res = (cm - gm) * inv * w + bb\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, num_groups=4, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, bias=bias)\n        self.group_norm = nn.GroupNorm(num_groups, out_channels)\n        self.num_groups = num_groups\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        B, C, D, H, W = x.shape\n        S = D * H * W\n        G = self.num_groups\n        CPG = C // G\n        eps = 1e-5\n        chmean = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        gmean = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        gvar = torch.empty((B * G,), device=x.device, dtype=x.dtype)\n        BLOCK = 1024\n        stats_kernel[(B * G,)](x, chmean, gmean, gvar, C, S, G, CPG,\n                               eps, BLOCK=BLOCK)\n        out = torch.empty((B, C), device=x.device, dtype=x.dtype)\n        w = self.group_norm.weight.contiguous()\n        b = self.group_norm.bias.contiguous()\n        grid = (triton.cdiv(B * C, BLOCK),)\n        final_kernel[grid](chmean, gmean, gvar, w, b, out, B, C, G, CPG,\n                           eps, BLOCK=BLOCK)\n        return out\n```", "L2_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_011": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_070 Gemm_Sigmoid_Scaling_ResidualAdd, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, n_elements, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elements\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = s * scaling + v\n    tl.store(out_ptr + offs, y, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, scaling_factor):\n        super().__init__()\n        self.gemm = nn.Linear(input_size, hidden_size)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_018": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_062 Matmul_GroupNorm_LeakyReLU_Sum, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef gn_kernel(x_ptr, w_ptr, b_ptr, out_ptr,\n              N, C, G, CG, eps, neg_slope,\n              BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    base = row * C + grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n    s = tl.sum(v, axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    rstd = 1.0 / tl.sqrt(var + eps)\n    coff = grp * CG + offs\n    w = tl.load(w_ptr + coff, mask=mask, other=0.0)\n    b = tl.load(b_ptr + coff, mask=mask, other=0.0)\n    y = (v - mean) * rstd * w + b\n    y = tl.where(y >= 0, y, y * neg_slope)\n    y = y + y\n    tl.store(out_ptr + base + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, hidden_size, num_groups, eps=1e-5, negative_slope=0.01):\n        super().__init__()\n        self.fc = nn.Linear(input_size, hidden_size)\n        self.gn = nn.GroupNorm(num_groups=num_groups, num_channels=hidden_size, eps=eps)\n        self.leaky_relu = nn.LeakyReLU(negative_slope=negative_slope)\n        self.num_groups = num_groups\n        self.hidden_size = hidden_size\n        self.eps = eps\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = self.fc(x).contiguous()\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        gn_kernel[grid](z, self.gn.weight, self.gn.bias, out,\n                        N, C, G, CG, self.eps, self.negative_slope,\n                        BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_022": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```", "L2_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_006 Conv3d_Softmax_MaxPool_MaxPool, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW,\n                 BLOCK_C: tl.constexpr, P: tl.constexpr):\n    pid = tl.program_id(0)\n    ow = pid % OW\n    tmp = pid // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    od = tmp % OD\n    n = tmp // OD\n\n    c = tl.arange(0, BLOCK_C)\n    cmask = c < C\n    maxv = tl.full((BLOCK_C,), -3.4e38, tl.float32)\n\n    n64 = n.to(tl.int64)\n    for kd in range(P):\n        for kh in range(P):\n            for kw in range(P):\n                id_ = od * P + kd\n                ih = oh * P + kh\n                iw = ow * P + kw\n                base = ((n64 * C + c.to(tl.int64)) * D + id_) * H\n                base = (base + ih) * W + iw\n                v = tl.load(x_ptr + base, mask=cmask, other=-3.4e38)\n                m = tl.max(v)\n                e = tl.exp(v - m)\n                ssum = tl.sum(tl.where(cmask, e, 0.0))\n                sv = e / ssum\n                maxv = tl.maximum(maxv, sv)\n\n    obase = ((n64 * C + c.to(tl.int64)) * OD + od) * OH\n    obase = (obase + oh) * OW + ow\n    tl.store(out_ptr + obase, maxv, mask=cmask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        P = self.pool_kernel_size * self.pool_kernel_size\n        OD = D // P\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OD, OH, OW), device=x.device, dtype=x.dtype)\n        BLOCK_C = 1\n        while BLOCK_C < C:\n            BLOCK_C *= 2\n        grid = (N * OD * OH * OW,)\n        fused_kernel[grid](x, out, N, C, D, H, W, OD, OH, OW,\n                           BLOCK_C=BLOCK_C, P=P)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_025": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_027": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_028": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Verified recipes for norm problems (speedups measured by the protected evaluator)\n- [3.98x on LayerNorm] For LayerNorm/RMSNorm over huge rows (few rows), split into two Triton kernels so the GPU stays saturated. First, a per-row stats kernel loops over the row in BLOCK=4096 chunks, accumulates sum and sum-of-squares in fp32, and stores mean and rstd. Second, a flat elementwise apply kernel (BLOCK=1024, grid=cdiv(numel,BLOCK)) computes row=off//N and col=off%N, loads mean/rstd/weight/bias, and writes (x-mean)*rstd*w+b. Keep the parameters in nn.LayerNorm and reuse its eps. Use contiguous views and fp32 accumulation.\n\n### A verified kernel for a related norm problem (L1_040 LayerNorm, 3.98x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef ln_stats_kernel(x_ptr, mean_ptr, rstd_ptr, N, eps,\n                    BLOCK: tl.constexpr):\n    row = tl.program_id(0)\n    x_ptr += row * N\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, N, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < N\n        v = tl.load(x_ptr + idx, mask=mask, other=0.0).to(tl.float32)\n        sum_ += tl.sum(v, axis=0)\n        sumsq += tl.sum(v * v, axis=0)\n    mean = sum_ / N\n    var = sumsq / N - mean * mean\n    rstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + row, mean)\n    tl.store(rstd_ptr + row, rstd)\n\n@triton.jit\ndef ln_apply_kernel(x_ptr, w_ptr, b_ptr, mean_ptr, rstd_ptr, out_ptr,\n                    N, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    off = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = off < total\n    row = off // N\n    col = off % N\n    x = tl.load(x_ptr + off, mask=mask, other=0.0).to(tl.float32)\n    mean = tl.load(mean_ptr + row, mask=mask, other=0.0)\n    rstd = tl.load(rstd_ptr + row, mask=mask, other=0.0)\n    w = tl.load(w_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    b = tl.load(b_ptr + col, mask=mask, other=0.0).to(tl.float32)\n    y = (x - mean) * rstd * w + b\n    tl.store(out_ptr + off, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, normalized_shape):\n        super().__init__()\n        self.ln = nn.LayerNorm(normalized_shape=normalized_shape)\n        self.eps = self.ln.eps\n\n    def forward(self, x):\n        x = x.contiguous()\n        ns = 1\n        for s in self.ln.normalized_shape:\n            ns *= s\n        rows = x.numel() // ns\n        N = ns\n        mean = torch.empty(rows, device=x.device, dtype=torch.float32)\n        rstd = torch.empty(rows, device=x.device, dtype=torch.float32)\n        xf = x.view(rows, N)\n        ln_stats_kernel[(rows,)](xf, mean, rstd, N, self.eps, BLOCK=4096)\n        out = torch.empty_like(x)\n        w = self.ln.weight.contiguous().view(-1)\n        b = self.ln.bias.contiguous().view(-1)\n        total = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(total, BLOCK),)\n        ln_apply_kernel[grid](x.view(-1), w, b, mean, rstd, out.view(-1),\n                              N, total, BLOCK=BLOCK)\n        return out\n```", "L2_029": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_086 Matmul_Divide_GELU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef div_gelu_kernel(x_ptr, out_ptr, inv_div, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * inv_div\n    y = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size, output_size, divisor):\n        super().__init__()\n        self.linear = nn.Linear(input_size, output_size)\n        self.divisor = divisor\n\n    def forward(self, x):\n        z = self.linear(x)\n        z = z.contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        div_gelu_kernel[grid](z, out, 1.0 / self.divisor, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_059 Matmul_Swish_Scaling, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef swish_scale_kernel(x_ptr, out_ptr, scale, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = 1.0 / (1.0 + tl.exp(-v))\n    y = v * s * scale\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        z = F.linear(x, self.matmul.weight, self.matmul.bias).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        swish_scale_kernel[grid](z, out, float(self.scaling_factor), n, BLOCK=BLOCK)\n        return out\n```", "L2_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_033": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_035": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_046 Conv2d_Subtract_Tanh_Subtract_AvgPool, 1.40x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, s1, s2, inv,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.zeros((BLOCK,), tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n            t = tl.extra.cuda.libdevice.tanh(v - s1) - s2\n            acc += t\n    acc = acc * inv\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract1_value, subtract2_value, kernel_size_pool):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract1_value = subtract1_value\n        self.subtract2_value = subtract2_value\n        self.kernel_size_pool = kernel_size_pool\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.kernel_size_pool\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, N, C, H, W, OH, OW, P,\n                           float(self.subtract1_value), float(self.subtract2_value),\n                           1.0 / (P * P), BLOCK=BLOCK)\n        return out\n```", "L2_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```", "L2_043": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_079 Conv3d_Multiply_InstanceNorm_Clamp_Multiply_Max, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef norm_kernel(x_ptr, out_ptr, mult_ptr, S, C,\n                clamp_min, clamp_max, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    c = pid % C\n    base = pid.to(tl.int64) * S\n    m = tl.load(mult_ptr + c)\n    sum_ = 0.0\n    sumsq = 0.0\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        sum_ += tl.sum(tl.where(mask, v, 0.0))\n        sumsq += tl.sum(tl.where(mask, v * v, 0.0))\n    mean = sum_ / S\n    var = sumsq / S - mean * mean\n    inv = 1.0 / tl.sqrt(var + eps)\n    for off in range(0, S, BLOCK):\n        idx = off + tl.arange(0, BLOCK)\n        mask = idx < S\n        v = tl.load(x_ptr + base + idx, mask=mask, other=0.0) * m\n        nrm = (v - mean) * inv\n        nrm = tl.minimum(tl.maximum(nrm, clamp_min), clamp_max) * m\n        tl.store(out_ptr + base + idx, nrm, mask=mask)\n\n\n@triton.jit\ndef max_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        acc = tl.maximum(acc, v)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, multiplier_shape, clamp_min, clamp_max):\n        super().__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.multiplier = nn.Parameter(torch.randn(multiplier_shape))\n        self.instance_norm = nn.InstanceNorm3d(out_channels)\n        self.clamp_min = clamp_min\n        self.clamp_max = clamp_max\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x)\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        x = x.contiguous()\n        mult = self.multiplier.reshape(-1).contiguous()\n        tmp = torch.empty_like(x)\n        BLOCK = 1024\n        norm_kernel[(N * C,)](x, tmp, mult, S, C,\n                              float(self.clamp_min), float(self.clamp_max),\n                              1e-5, BLOCK=BLOCK)\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        grid = (triton.cdiv(NS, BLOCK),)\n        max_kernel[grid](tmp, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_008 Conv3d_Divide_Max_GlobalAvgPool_BiasAdd_Sum, 1.07x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                inv_div, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # (n*C + c)\n    base = pid.to(tl.int64) * S\n    nwin = Dp * Hp * Wp\n    acc = 0.0\n    for wstart in range(0, nwin, BLOCK):\n        widx = wstart + tl.arange(0, BLOCK)\n        wmask = widx < nwin\n        dwi = widx // (Hp * Wp)\n        rem = widx % (Hp * Wp)\n        hwi = rem // Wp\n        wwi = rem % Wp\n        d0 = dwi * pd\n        h0 = hwi * ph\n        w0 = wwi * pw\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(pd):\n            for kh in range(ph):\n                for kw in range(pw):\n                    dd = d0 + kd\n                    hh = h0 + kh\n                    ww = w0 + kw\n                    off = dd.to(tl.int64) * (H * W) + hh * W + ww\n                    v = tl.load(x_ptr + base + off, mask=wmask, other=-1e30)\n                    m = tl.maximum(m, v)\n        acc += tl.sum(tl.where(wmask, m, 0.0))\n    avg = acc * inv_div / nwin\n    tl.store(out_ptr + pid, avg)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, divisor, pool_size, bias_shape, sum_dim):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.divisor = divisor\n        self.pool_size = pool_size\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.sum_dim = sum_dim\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        pd, ph, pw = self.pool_size\n        Dp, Hp, Wp = D // pd, H // ph, W // pw\n        S = D * H * W\n        perc = torch.empty((N * C,), device=x.device, dtype=x.dtype)\n        BLOCK = 256\n        pool_kernel[(N * C,)](x, perc, C, D, H, W, Dp, Hp, Wp, pd, ph, pw,\n                              1.0 / self.divisor, S, BLOCK=BLOCK)\n        perc = perc.view(N, C)\n        bias_sum = self.bias.view(-1).sum()\n        out = perc.sum(dim=1) + bias_sum\n        return out.view(N, 1, 1, 1)\n```", "L2_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_047": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_048": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_047 Conv3d_Mish_Tanh, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef mish_tanh_kernel(x_ptr, out_ptr, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < N\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(x))\n    mish = x * tl.extra.cuda.libdevice.tanh(sp)\n    out = tl.extra.cuda.libdevice.tanh(mish)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(N, BLOCK),)\n        mish_tanh_kernel[grid](x, out, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_050": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_003 ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU, 1.26x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef ln_kernel(x_ptr, out_ptr, w_ptr, b_ptr, sw, W, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0).to(tl.int64)\n    offs = tl.arange(0, BLOCK)\n    m = offs < W\n    base = pid * W\n    v = tl.load(x_ptr + base + offs, mask=m, other=0.0) + sw\n    mean = tl.sum(v, axis=0) / W\n    d = tl.where(m, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / W\n    rstd = 1.0 / tl.sqrt(var + eps)\n    w = tl.load(w_ptr + offs, mask=m, other=0.0)\n    b = tl.load(b_ptr + offs, mask=m, other=0.0)\n    r = d * rstd * w + b\n    tl.store(out_ptr + base + offs, r, mask=m)\n\n\n@triton.jit\ndef pool_gelu_kernel(x_ptr, out_ptr, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    nc = t // OD\n\n    acc = tl.zeros((BLOCK,), tl.float32)\n    for dz in tl.static_range(2):\n        for dy in tl.static_range(2):\n            for dx in tl.static_range(2):\n                iz = od * 2 + dz\n                iy = oh * 2 + dy\n                ix = ow * 2 + dx\n                in_off = ((nc * D + iz) * H + iy) * W + ix\n                v = tl.load(x_ptr + in_off, mask=mask, other=0.0)\n                acc += v\n    acc = acc * 0.125\n    gelu = acc * 0.5 * (1.0 + tl.erf(acc * 0.70710678118654752440))\n    tl.store(out_ptr + idx64, gelu, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, sum_weight, norm_shape, pool_kernel_size):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.sum_weight = nn.Parameter(torch.tensor(sum_weight))\n        self.norm = nn.LayerNorm(norm_shape)\n        self.avg_pool = nn.AvgPool3d(kernel_size=pool_kernel_size)\n        self.gelu = nn.GELU()\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        rows = N * C * D * H\n        c2 = c.view(rows, W)\n        normed = torch.empty_like(c2)\n        BLOCKW = triton.next_power_of_2(W)\n        w = self.norm.weight.contiguous()\n        b = self.norm.bias.contiguous()\n        ln_kernel[(rows,)](c2, normed, w, b, float(self.sum_weight.item()), W, self.norm.eps, BLOCK=BLOCKW)\n        normed = normed.view(N, C, D, H, W)\n\n        OD, OH, OW = D // 2, H // 2, W // 2\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        pool_gelu_kernel[grid](normed, out, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_052": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_057": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```", "L2_061": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_067": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```", "L2_069": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_071": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_067 Conv2d_GELU_GlobalAvgPool, 1.30x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra import libdevice\n\n\n@triton.jit\ndef gelu_avg_kernel(x_ptr, out_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    base = pid.to(tl.int64) * S\n    acc = 0.0\n    for off in range(0, S, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < S\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        g = 0.5 * v * (1.0 + libdevice.erf(v * 0.7071067811865476))\n        acc += tl.sum(g, axis=0)\n    tl.store(out_ptr + pid, acc / S)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, C), device=x.device, dtype=x.dtype)\n        grid = (N * C,)\n        gelu_avg_kernel[grid](x, out, S, BLOCK=1024)\n        return out\n```", "L2_073": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_082 Conv2d_Tanh_Scaling_BiasAdd_Max, 1.94x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, out_ptr,\n                 N, C, H, W, OH, OW, P, scaling,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    TOTAL = N * C * OH * OW\n    mask = offs < TOTAL\n\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -1e30, tl.float32)\n    base = (n.to(tl.int64) * C + c) * H * W\n    for ph in range(P):\n        for pw in range(P):\n            h = h0 + ph\n            w = w0 + pw\n            idx = base + h.to(tl.int64) * W + w\n            v = tl.load(x_ptr + idx, mask=mask, other=-1e30)\n            t = tl.extra.cuda.libdevice.tanh(v)\n            t = t * scaling + b\n            acc = tl.maximum(acc, t)\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = scaling_factor\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.pool_kernel_size = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_kernel_size\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=x.dtype)\n        TOTAL = N * C * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.bias.contiguous().view(-1), out,\n                           N, C, H, W, OH, OW, P, float(self.scaling_factor),\n                           BLOCK=BLOCK)\n        return out\n```", "L2_074": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_089 ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max, 1.06x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, sub_ptr, out_ptr, N, C, S, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = idx < total\n\n    # idx indexes (n, s) flat where s in [0,S)\n    n = idx // S\n    s = idx % S\n    base = n * C * S + s\n\n    # pass 1: max over channels\n    mx = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=-1e30)\n        mx = tl.maximum(mx, v)\n\n    # pass 2: sum of exp\n    sm = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sm += tl.exp(v - mx)\n\n    # pass 3: softmax, subtract, swish, max over channels\n    res = tl.full((BLOCK,), -1e30, tl.float32)\n    for c in range(0, C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        sub = tl.load(sub_ptr + c)\n        sm_val = tl.exp(v - mx) / sm\n        y = sm_val - sub\n        swish = (tl.sigmoid(y) * y)\n        res = tl.maximum(res, swish)\n\n    tl.store(out_ptr + idx, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, output_padding, pool_kernel_size, pool_stride, pool_padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, output_padding=output_padding)\n        self.max_pool = nn.MaxPool3d(kernel_size=pool_kernel_size, stride=pool_stride, padding=pool_padding)\n        self.subtract = nn.Parameter(torch.randn(out_channels))\n\n    def forward(self, x):\n        x = self.conv_transpose(x)\n        x = self.max_pool(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        total = N * S\n\n        out = torch.empty((N, D, H, W), device=x.device, dtype=x.dtype)\n        sub = self.subtract.contiguous()\n\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](x, sub, out, N, C, S, total, BLOCK=BLOCK)\n        return out\n```", "L2_075": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_094 Gemm_BiasAdd_Hardtanh_Mish_GroupNorm, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, bias_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, G, CG, eps,\n                 BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid // G\n    grp = pid % G\n    col0 = grp * CG\n    offs = tl.arange(0, BLOCK)\n    mask = offs < CG\n    chan = col0 + offs\n    idx = row * C + chan\n\n    v = tl.load(x_ptr + idx, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + chan, mask=mask, other=0.0)\n    v = v + b\n    # hardtanh [-1,1]\n    v = tl.minimum(tl.maximum(v, -1.0), 1.0)\n    # mish: v * tanh(softplus(v))\n    sp = tl.log(1.0 + tl.exp(v))\n    v = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n\n    # group norm stats\n    s = tl.sum(tl.where(mask, v, 0.0), axis=0)\n    mean = s / CG\n    d = tl.where(mask, v - mean, 0.0)\n    var = tl.sum(d * d, axis=0) / CG\n    inv = 1.0 / tl.sqrt(var + eps)\n    g = tl.load(gamma_ptr + chan, mask=mask, other=0.0)\n    bt = tl.load(beta_ptr + chan, mask=mask, other=0.0)\n    out = (v - mean) * inv * g + bt\n    tl.store(out_ptr + idx, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape, num_groups):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.hardtanh = nn.Hardtanh()\n        self.mish = nn.Mish()\n        self.groupnorm = nn.GroupNorm(num_groups=num_groups, num_channels=out_features)\n        self.num_groups = num_groups\n        self.out_features = out_features\n\n    def forward(self, x):\n        z = self.gemm(x)\n        N, C = z.shape\n        G = self.num_groups\n        CG = C // G\n        out = torch.empty_like(z)\n        BLOCK = triton.next_power_of_2(CG)\n        grid = (N * G,)\n        fused_kernel[grid](\n            z, self.bias, self.groupnorm.weight, self.groupnorm.bias, out,\n            N, C, G, CG, float(self.groupnorm.eps),\n            BLOCK=BLOCK,\n        )\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_076 Gemm_Add_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bias_relu_kernel(x_ptr, bias_ptr, out_ptr, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + col, mask=mask, other=0.0)\n    y = tl.maximum(v + b, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias_shape):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=False)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        z = torch.mm(x, self.gemm.weight.t())\n        M, N = z.shape\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        bias_relu_kernel[grid](z, self.bias, out, M, N, BLOCK=BLOCK)\n        return out\n```", "L2_076": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_041 Gemm_BatchNorm_GELU_ReLU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr,\n                 eps, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    # gelu\n    g = 0.5 * y * (1.0 + tl.erf(y * 0.7071067811865476))\n    # relu\n    g = tl.maximum(g, 0.0)\n    tl.store(out_ptr + offs, g, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.batch_norm = nn.BatchNorm1d(out_features)\n        self.eps = 1e-5\n        self.momentum = 0.1\n\n    def forward(self, x):\n        z = self.gemm(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=2048)\n\n        if self.training:\n            with torch.no_grad():\n                self.batch_norm.running_mean.mul_(1 - self.momentum).add_(self.momentum * mean)\n                unbiased = var * (M / (M - 1))\n                self.batch_norm.running_var.mul_(1 - self.momentum).add_(self.momentum * unbiased)\n                self.batch_norm.num_batches_tracked.add_(1)\n            use_mean, use_var = mean, var\n        else:\n            use_mean = self.batch_norm.running_mean\n            use_var = self.batch_norm.running_var\n\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, use_mean, use_var, self.batch_norm.weight,\n                           self.batch_norm.bias, self.eps, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_012 Gemm_Multiply_LeakyReLU, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, mult, neg_slope, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    v = v * mult\n    v = tl.where(v >= 0, v, v * neg_slope)\n    tl.store(out_ptr + offs, v, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, multiplier, negative_slope):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.multiplier = multiplier\n        self.negative_slope = negative_slope\n\n    def forward(self, x):\n        z = torch.addmm(self.gemm.bias, x, self.gemm.weight.t())\n        n = z.numel()\n        out = torch.empty_like(z)\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        fused_kernel[grid](z, out, self.multiplier, self.negative_slope, n, BLOCK=BLOCK)\n        return out\n```", "L2_077": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n- [1.06x on ConvTranspose3d_MaxPool_Softmax_Subtract_Swish_Max] Keep ConvTranspose3d (and MaxPool3d) in cuDNN via torch and call .contiguous() on the result. Fuse all channel-wise epilogues (softmax over C, per-channel bias/subtract, activation, reduction over C) into one Triton kernel. Map one lane per (n, spatial) position with a flat 1D grid and BLOCK=256. Loop over the C channels with stride-S loads, so consecutive lanes read consecutive spatial addresses (coalesced). Use a stable 3-pass softmax (max, sum-exp, normalize+epilogue) in fp32. Re-reads hit L1/L2. Write only the reduced output.\n\n### A verified kernel for a related conv_transpose problem (L2_072 ConvTranspose3d_BatchNorm_AvgPool_AvgPool, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef pool_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr,\n                N, C, D, H, W, OD, OH, OW, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    total = N * C * OD * OH * OW\n    mask = offs < total\n    o = offs.to(tl.int64)\n    ow = o % OW\n    t = o // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    t = t // OD\n    c = t % C\n    n = t // C\n\n    sc = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n\n    HW = H * W\n    DHW = D * HW\n    base = (n * C + c) * DHW\n\n    acc = tl.zeros((BLOCK,), dtype=tl.float32)\n    for dd in tl.static_range(4):\n        for hh in tl.static_range(4):\n            for ww in tl.static_range(4):\n                id_ = od * 4 + dd\n                ih = oh * 4 + hh\n                iw = ow * 4 + ww\n                addr = base + id_ * HW + ih * W + iw\n                v = tl.load(x_ptr + addr, mask=mask, other=0.0)\n                acc += v\n    acc = acc * (1.0 / 64.0)\n    r = sc * acc + sh\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias_shape):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        M = N * S\n        mean_c = ssum_nc.sum(0) / M\n        var_c = ssq_nc.sum(0) / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)\n        shift_c = self.batch_norm.bias - scale_c * mean_c\n\n        OD = D // 4\n        OH = H // 4\n        OW = W // 4\n        out = torch.empty((N, C, OD, OH, OW), device=c.device, dtype=torch.float32)\n        total = N * C * OD * OH * OW\n        BLOCK = 256\n        grid = (triton.cdiv(total, BLOCK),)\n        cc = c.contiguous()\n        pool_kernel[grid](cc, out, scale_c.contiguous(), shift_c.contiguous(),\n                          N, C, D, H, W, OD, OH, OW, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```", "L2_079": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_043 Conv3d_Max_LogSumExp_ReLU, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, Dp, Hp, Wp,\n                 NOUT, BLOCK: tl.constexpr, C_CONST: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NOUT\n    npw = Hp * Wp\n    nplane = Dp * npw\n    n = offs // nplane\n    rem = offs % nplane\n    dp = rem // npw\n    rem2 = rem % npw\n    hp = rem2 // Wp\n    wp = rem2 % Wp\n    d0 = dp * 2\n    h0 = hp * 2\n    w0 = wp * 2\n    HW = H * W\n    S = D * HW\n    nbase = n.to(tl.int64) * C * S\n\n    run_max = tl.full((BLOCK,), -1e30, tl.float32)\n    run_sum = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C_CONST):\n        cbase = nbase + c * S\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for kd in range(2):\n            for kh in range(2):\n                for kw in range(2):\n                    off = cbase + (d0 + kd).to(tl.int64) * HW + (h0 + kh) * W + (w0 + kw)\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        new_max = tl.maximum(run_max, m)\n        run_sum = run_sum * tl.exp(run_max - new_max) + tl.exp(m - new_max)\n        run_max = new_max\n    lse = run_max + tl.log(run_sum)\n    lse = tl.maximum(lse, 0.0)\n    tl.store(out_ptr + offs, lse, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n        self.out_channels = out_channels\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        Dp, Hp, Wp = D // 2, H // 2, W // 2\n        out = torch.empty((N, 1, Dp, Hp, Wp), device=x.device, dtype=x.dtype)\n        NOUT = N * Dp * Hp * Wp\n        BLOCK = 256\n        grid = (triton.cdiv(NOUT, BLOCK),)\n        fused_kernel[grid](x, out, N, C, D, H, W, Dp, Hp, Wp,\n                           NOUT, BLOCK=BLOCK, C_CONST=C)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_048 Conv3d_Scaling_Tanh_Multiply_Sigmoid, 1.33x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, scale_ptr, bias_ptr, out_ptr,\n                 TOTAL, C, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    b = tl.load(bias_ptr + c, mask=mask, other=0.0)\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    t = tl.extra.cuda.libdevice.tanh(x * s)\n    t = t * b\n    out = 1.0 / (1.0 + tl.exp(-t))\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor, bias_shape):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)\n        self.scaling_factor = nn.Parameter(torch.randn(bias_shape))\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, D, H, W = x.shape\n        S = D * H * W\n        TOTAL = x.numel()\n        out = torch.empty_like(x)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, self.scaling_factor.contiguous().view(-1),\n                           self.bias.contiguous().view(-1), out,\n                           TOTAL, C, S, BLOCK=BLOCK)\n        return out\n```", "L2_082": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_073 Conv2d_BatchNorm_Scaling, 1.68x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef stats_kernel2(x_ptr, sum_ptr, sumsq_ptr, N, C, S, SBLK: tl.constexpr):\n    c = tl.program_id(0)\n    sblk = tl.program_id(1)\n    offs = sblk * SBLK + tl.arange(0, SBLK)\n    smask = offs < S\n    acc_sum = tl.zeros((SBLK,), tl.float32)\n    acc_sq = tl.zeros((SBLK,), tl.float32)\n    cS = c.to(tl.int64) * S\n    NCS = C * S\n    for n in range(N):\n        base = n.to(tl.int64) * NCS + cS + offs\n        v = tl.load(x_ptr + base, mask=smask, other=0.0)\n        acc_sum += v\n        acc_sq += v * v\n    s = tl.sum(acc_sum, axis=0)\n    sq = tl.sum(acc_sq, axis=0)\n    tl.atomic_add(sum_ptr + c, s)\n    tl.atomic_add(sumsq_ptr + c, sq)\n\n\n@triton.jit\ndef bn_apply_kernel(x_ptr, out_ptr, mean_ptr, invstd_ptr, w_ptr, b_ptr,\n                    scaling, C, S, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    c = (offs // S) % C\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + c, mask=mask, other=0.0)\n    invstd = tl.load(invstd_ptr + c, mask=mask, other=0.0)\n    w = tl.load(w_ptr + c, mask=mask, other=0.0)\n    b = tl.load(b_ptr + c, mask=mask, other=0.0)\n    r = ((v - mean) * invstd * w + b) * scaling\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scaling_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.bn = nn.BatchNorm2d(out_channels)\n        self.scaling_factor = scaling_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        count = N * S\n        device = x.device\n\n        sums = torch.zeros(C, device=device, dtype=torch.float32)\n        sumsq = torch.zeros(C, device=device, dtype=torch.float32)\n        SBLK = 1024\n        nsblk = triton.cdiv(S, SBLK)\n        stats_kernel2[(C, nsblk)](x, sums, sumsq, N, C, S, SBLK=SBLK)\n\n        if self.training:\n            mean = sums / count\n            var = sumsq / count - mean * mean\n            with torch.no_grad():\n                self.bn.running_mean.mul_(1 - self.bn.momentum).add_(self.bn.momentum * mean.detach())\n                unbiased = var * count / (count - 1)\n                self.bn.running_var.mul_(1 - self.bn.momentum).add_(self.bn.momentum * unbiased.detach())\n        else:\n            mean = self.bn.running_mean\n            var = self.bn.running_var\n\n        invstd = torch.rsqrt(var + self.bn.eps)\n        w = self.bn.weight\n        b = self.bn.bias\n\n        out = torch.empty_like(x)\n        TOTAL = x.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        bn_apply_kernel[grid](x, out, mean.contiguous(), invstd.contiguous(),\n                              w.contiguous(), b.contiguous(),\n                              float(self.scaling_factor), C, S, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_032 Conv2d_Scaling_Min, 1.10x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef scale_min_kernel(x_ptr, out_ptr, scale, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = acc * scale\n    tl.store(out_ptr + offs, acc, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, scale_factor):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.scale_factor = scale_factor\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        scale_min_kernel[grid](x, out, float(self.scale_factor), C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_085": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.37x on Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp] Keep the conv in cuDNN via torch. Replace the GroupNorm+pointwise+channel-reduction tail with two Triton kernels. (1) A stats kernel with one program per (n, group): the group is a contiguous CPG*S slice, so loop BLOCK=1024 accumulating sum and sum-of-squares in fp32, then emit mean and invstd. (2) A fused kernel with one thread per (n, spatial) position and BLOCK=256 coalesced along spatial. Loop over channels with stride S, normalize, apply the activations, add the residual, and compute a two-pass max/sum-exp logsumexp. Recompute instead of storing intermediates. Use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n\n### A verified kernel for a related conv problem (L2_035 Conv2d_Subtract_HardSwish_MaxPool_Mish, 1.27x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, sub, N, C, H, W, OH, OW, P, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    ow = offs % OW\n    tmp = offs // OW\n    oh = tmp % OH\n    tmp = tmp // OH\n    c = tmp % C\n    n = tmp // C\n\n    base = (n.to(tl.int64) * C + c) * H * W\n    h0 = oh * P\n    w0 = ow * P\n    acc = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for ph in range(0, P):\n        for pw in range(0, P):\n            ih = h0 + ph\n            iw = w0 + pw\n            vmask = mask & (ih < H) & (iw < W)\n            v = tl.load(x_ptr + base + ih.to(tl.int64) * W + iw, mask=vmask, other=-3.4e38)\n            v = v - sub\n            hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n            acc = tl.maximum(acc, hs)\n    # mish: x * tanh(softplus(x))\n    sp = tl.log(1.0 + tl.exp(acc))\n    th = (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    res = acc * th\n    tl.store(out_ptr + offs, res, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, subtract_value, pool_kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.subtract_value = subtract_value\n        self.pool_k = pool_kernel_size\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        P = self.pool_k\n        OH = H // P\n        OW = W // P\n        out = torch.empty((N, C, OH, OW), device=x.device, dtype=torch.float32)\n        TOTAL = out.numel()\n        BLOCK = 256\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        fused_kernel[grid](x, out, float(self.subtract_value),\n                           N, C, H, W, OH, OW, P, TOTAL, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related conv problem (L2_092 Conv2d_GroupNorm_Tanh_HardSwish_ResidualAdd_LogSumExp, 2.37x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\nfrom triton.language.extra.cuda import libdevice\n\n\n@triton.jit\ndef gn_stats_kernel(x_ptr, mean_ptr, invstd_ptr, CPG, S, GS, eps, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)  # over n*groups\n    base = pid.to(tl.int64) * GS\n    acc = 0.0\n    acc2 = 0.0\n    for off in range(0, GS, BLOCK):\n        offs = off + tl.arange(0, BLOCK)\n        mask = offs < GS\n        v = tl.load(x_ptr + base + offs, mask=mask, other=0.0)\n        acc += tl.sum(v, axis=0)\n        acc2 += tl.sum(v * v, axis=0)\n    mean = acc / GS\n    var = acc2 / GS - mean * mean\n    invstd = 1.0 / tl.sqrt(var + eps)\n    tl.store(mean_ptr + pid, mean)\n    tl.store(invstd_ptr + pid, invstd)\n\n\n@triton.jit\ndef fused_kernel(x_ptr, mean_ptr, invstd_ptr, gamma_ptr, beta_ptr, out_ptr,\n                 N, C, S, NS, G, CPG, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    maxv = tl.full((BLOCK,), -3.4e38, tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        maxv = tl.maximum(maxv, res)\n    sumexp = tl.zeros((BLOCK,), tl.float32)\n    for c in range(C):\n        g = c // CPG\n        ng = n * G + g\n        xc = tl.load(x_ptr + base + c * S, mask=mask, other=0.0)\n        mean = tl.load(mean_ptr + ng, mask=mask, other=0.0)\n        invstd = tl.load(invstd_ptr + ng, mask=mask, other=0.0)\n        gamma = tl.load(gamma_ptr + c)\n        beta = tl.load(beta_ptr + c)\n        norm = (xc - mean) * invstd * gamma + beta\n        t = libdevice.tanh(norm)\n        hs = t * tl.minimum(tl.maximum(t + 3.0, 0.0), 6.0) / 6.0\n        res = xc + hs\n        sumexp += tl.exp(res - maxv)\n    out = maxv + tl.log(sumexp)\n    tl.store(out_ptr + offs, out, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, groups, eps=1e-5):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n        self.group_norm = nn.GroupNorm(groups, out_channels, eps=eps)\n        self.tanh = nn.Tanh()\n        self.hard_swish = nn.Hardswish()\n        self.groups = groups\n        self.eps = eps\n\n    def forward(self, x):\n        x_conv = self.conv(x).contiguous()\n        N, C, H, W = x_conv.shape\n        S = H * W\n        G = self.groups\n        CPG = C // G\n        GS = CPG * S\n        mean = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        invstd = torch.empty((N * G,), device=x_conv.device, dtype=torch.float32)\n        gn_stats_kernel[(N * G,)](x_conv, mean, invstd, CPG, S, GS, self.eps, BLOCK=1024)\n        out = torch.empty((N, 1, H, W), device=x_conv.device, dtype=x_conv.dtype)\n        NS = N * S\n        BLOCK = 256\n        grid = (triton.cdiv(NS, BLOCK),)\n        fused_kernel[grid](x_conv, mean, invstd,\n                           self.group_norm.weight, self.group_norm.bias,\n                           out, N, C, S, NS, G, CPG, BLOCK=BLOCK)\n        return out\n```", "L2_086": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_097 Matmul_BatchNorm_BiasAdd_Divide_Swish, 1.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef stats_kernel(x_ptr, mean_ptr, var_ptr, M, N, BLOCK_M: tl.constexpr):\n    col = tl.program_id(0)\n    offs = tl.arange(0, BLOCK_M)\n    acc = tl.zeros((), dtype=tl.float32)\n    acc2 = tl.zeros((), dtype=tl.float32)\n    for start in range(0, M, BLOCK_M):\n        idx = start + offs\n        mask = idx < M\n        v = tl.load(x_ptr + idx * N + col, mask=mask, other=0.0)\n        acc += tl.sum(v)\n        acc2 += tl.sum(v * v)\n    mean = acc / M\n    var = acc2 / M - mean * mean\n    tl.store(mean_ptr + col, mean)\n    tl.store(var_ptr + col, var)\n\n@triton.jit\ndef apply_kernel(x_ptr, out_ptr, mean_ptr, var_ptr, gamma_ptr, beta_ptr, bias_ptr,\n                 eps, divide_value, M, N, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < M * N\n    col = offs % N\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    mean = tl.load(mean_ptr + col, mask=mask, other=0.0)\n    var = tl.load(var_ptr + col, mask=mask, other=0.0)\n    gamma = tl.load(gamma_ptr + col, mask=mask, other=0.0)\n    beta = tl.load(beta_ptr + col, mask=mask, other=0.0)\n    bias = tl.load(bias_ptr)\n    inv = 1.0 / tl.sqrt(var + eps)\n    y = (v - mean) * inv * gamma + beta\n    y = (y + bias) / divide_value\n    y = y * (1.0 / (1.0 + tl.exp(-y)))\n    tl.store(out_ptr + offs, y, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bn_eps=1e-5, bn_momentum=0.1, bias_shape=(1,), divide_value=1.0):\n        super().__init__()\n        self.matmul = nn.Linear(in_features, out_features)\n        self.bn = nn.BatchNorm1d(out_features, eps=bn_eps, momentum=bn_momentum)\n        self.bias = nn.Parameter(torch.randn(bias_shape))\n        self.divide_value = divide_value\n        self.bn_eps = bn_eps\n        self.bn_momentum = bn_momentum\n\n    def forward(self, x):\n        z = self.matmul(x).contiguous()\n        M, N = z.shape\n        mean = torch.empty(N, device=z.device, dtype=torch.float32)\n        var = torch.empty(N, device=z.device, dtype=torch.float32)\n        stats_kernel[(N,)](z, mean, var, M, N, BLOCK_M=1024)\n\n        with torch.no_grad():\n            self.bn.running_mean.mul_(1 - self.bn_momentum).add_(self.bn_momentum * mean)\n            unbiased = var * (M / (M - 1))\n            self.bn.running_var.mul_(1 - self.bn_momentum).add_(self.bn_momentum * unbiased)\n            self.bn.num_batches_tracked.add_(1)\n\n        out = torch.empty_like(z)\n        bias_flat = self.bias.reshape(-1)\n        BLOCK = 1024\n        grid = (triton.cdiv(M * N, BLOCK),)\n        apply_kernel[grid](z, out, mean, var, self.bn.weight, self.bn.bias, bias_flat,\n                           self.bn_eps, self.divide_value, M, N, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L2_089": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv_transpose problems (wrong results or slower than eager)\n- Pitfall: Avoid launching a per-forward weight-transform kernel (flip/transpose) before a library call. Cache the transformed weight once, or fuse the transform, since extra launches and memory traffic make it slower than eager.\n- Pitfall: Don'...'s native transposed conv is usually as fast or faster, so this measured slower.\n- Pitfall: In Triton kernels over large tensors (e.g. 3D conv outputs), compute offsets in int64 (cast program_id/indices with .to(tl.int64)). int32 products like n*C*S can overflow and crash, leaving no output during timing.\n- Pitfall: Never launch a pure copy/identity kernel into a fresh buffer just to have a custom kernel; that adds a full memory round-trip and guarantees slowdown versus eager.\n- Pitfall: Don't rewrite conv_transpose as flipped-weight F.conv2d plus a separate elementwise kernel; the per-call weight flip and extra full-output pass make it slower. Fuse bias into a real kernel, or skip pointless copies.\n\n### Verified recipes for conv_transpose problems (speedups measured by the protected evaluator)\n- [2.29x on conv_transposed_2D_asymmetric_input_asymmetric_kernel___padded__] For stride-1 transposed conv, rewrite it as a regular cuDNN conv2d: build the weight with a tiny Triton kernel that swaps the IC/OC axes and flips KH/KW, (IC,OC,KH,KW)->(OC,IC,KH-1-kh,KW-1-kw). Then call F.conv2d with padding=(K-1-p) per dimension and pass the bias through. cuDNN's forward conv path is much faster than ConvTranspose's dgrad path. Keep the math in fp32 so it is exact. For stride>1, groups, dilation or output_padding, fall back to nn.ConvTranspose2d. Cache the flipped weight if it is static.\n- [1.68x on ConvTranspose3d_BatchNorm_AvgPool_AvgPool] Keep the ConvTranspose in cuDNN via torch. Fold training-mode BatchNorm into a per-channel affine: one Triton program per (n,c) row loops over contiguous spatial data in 1024-wide blocks, accumulating fp32 sum and sum-of-squares. Finish mean/var/scale/shift with tiny torch ops. Because BN is affine, apply it after pooling: replace the two 2x pools with one fused 4x4x4 average kernel. Use one thread per output, int64 index math, static_range unrolled loads, and scale*avg+shift at store.\n- [1.32x on ConvTranspose3d_BatchNorm_Subtract] Keep ConvTranspose in cuDNN via torch. Fuse everything after it into two Triton passes over the contiguous (N*C, S) view. Pass 1: one program per (n,c) row, loop over S in 1024-element blocks, accumulate fp32 sum and sum-of-squares. Finish the tiny per-channel math in torch: batch mean/var (training-mode BN) and scale = gamma/sqrt(var+eps). Pass 2: write scale*(x - row_mean) in one read-modify-write sweep. BN's beta, shift and the conv bias cancel algebraically, so fold them away. fp32 accumulation meets 1e-4.\n- [1.26x on ConvTranspose3d_Sum_LayerNorm_AvgPool_GELU] Keep ConvTranspose in cuDNN via torch and fuse only the epilogue in Triton. LayerNorm normalises the last dim (W), not channels, so treat the output as a 2D [rows, W] view. Launch one program per row with BLOCK=next_pow2(W), add scalar bias before the mean, take a two-pass variance in fp32, and compute rstd as 1/sqrt(var+eps). Then run a second elementwise kernel fusing avgpool (static_range window loads, multiply by 1/k) with exact erf-GELU. Use int64 index math. Better still, fuse LN into the pool kernel to avoid the intermediate write.\n- [1.26x on ConvTranspose3d_LeakyReLU_Multiply_LeakyReLU_Max] Keep the ConvTranspose3d itself in cuDNN via nn.ConvTranspose3d and fuse the entire epilogue into one Triton kernel that reads the conv output once: LeakyReLU, per-channel scale, LeakyReLU, MaxPool. Launch one thread per pooled output element over a flat index (BLOCK=256, 1D grid). Decode n\u00b7c/od/oh/ow with div/mod, load the per-channel multiplier once, and unroll the 2x2x2 window with tl.static_range. Use tl.where for the slopes and a -1e30 init for max. Keep all math fp32, which stays within 1e-4.\n\n### A verified kernel for a related conv_transpose problem (L2_015 ConvTranspose3d_BatchNorm_Subtract, 1.32x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef reduce_kernel(x_ptr, sum_ptr, sqsum_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    acc = tl.zeros((), dtype=tl.float32)\n    accsq = tl.zeros((), dtype=tl.float32)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        acc += tl.sum(v)\n        accsq += tl.sum(v * v)\n    tl.store(sum_ptr + pid, acc)\n    tl.store(sqsum_ptr + pid, accsq)\n\n\n@triton.jit\ndef out_kernel(x_ptr, out_ptr, scale_ptr, smean_ptr, S, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    base = pid * S\n    sc = tl.load(scale_ptr + pid)\n    sm = tl.load(smean_ptr + pid)\n    for i in range(0, S, BLOCK):\n        idx = i + offs\n        m = idx < S\n        v = tl.load(x_ptr + base + idx, mask=m, other=0.0)\n        r = sc * (v - sm)\n        tl.store(out_ptr + base + idx, r, mask=m)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding, bias=True):\n        super(ModelNew, self).__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, bias=bias)\n        self.batch_norm = nn.BatchNorm3d(out_channels)\n\n    def forward(self, x):\n        c = self.conv_transpose(x)\n        N, C, D, H, W = c.shape\n        S = D * H * W\n        c2 = c.contiguous().view(N * C, S)\n\n        ssum = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        ssq = torch.empty(N * C, device=c.device, dtype=torch.float32)\n        reduce_kernel[(N * C,)](c2, ssum, ssq, S, BLOCK=1024)\n\n        ssum_nc = ssum.view(N, C)\n        ssq_nc = ssq.view(N, C)\n        total_sum = ssum_nc.sum(0)\n        total_sq = ssq_nc.sum(0)\n        M = N * S\n        mean_c = total_sum / M\n        var_c = total_sq / M - mean_c * mean_c\n        scale_c = self.batch_norm.weight / torch.sqrt(var_c + self.batch_norm.eps)  # (C,)\n\n        scale_nc = scale_c.unsqueeze(0).expand(N, C).contiguous().view(N * C)\n        smean_nc = (ssum_nc / S).contiguous().view(N * C)\n\n        out = torch.empty_like(c2)\n        out_kernel[(N * C,)](c2, out, scale_nc, smean_nc, S, BLOCK=1024)\n        return out.view(N, C, D, H, W)\n```\n\n### A verified kernel for a related conv_transpose problem (L2_078 ConvTranspose3d_Max_Max_Sum, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef fused_kernel(x_ptr, out_ptr, N, C, D, H, W, OD, OH, OW, total, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    idx = pid * BLOCK + tl.arange(0, BLOCK)\n    idx64 = idx.to(tl.int64)\n    mask = idx < total\n\n    ow = idx64 % OW\n    t = idx64 // OW\n    oh = t % OH\n    t = t // OH\n    od = t % OD\n    n = t // OD\n\n    d0 = od * 6\n    h0 = oh * 6\n    w0 = ow * 6\n\n    C64 = C.to(tl.int64)\n    D64 = D.to(tl.int64)\n    H64 = H.to(tl.int64)\n    W64 = W.to(tl.int64)\n\n    s = tl.zeros((BLOCK,), tl.float32)\n    for c in range(0, C):\n        base_nc = (n * C64 + c) * D64\n        m = tl.full((BLOCK,), -1e30, tl.float32)\n        for dz in tl.static_range(6):\n            iz = d0 + dz\n            for dy in tl.static_range(6):\n                iy = h0 + dy\n                for dx in tl.static_range(6):\n                    ix = w0 + dx\n                    off = ((base_nc + iz) * H64 + iy) * W64 + ix\n                    v = tl.load(x_ptr + off, mask=mask, other=-1e30)\n                    m = tl.maximum(m, v)\n        s += m\n    tl.store(out_ptr + idx64, s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):\n        super().__init__()\n        self.conv_transpose = nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=stride, padding=padding)\n\n    def forward(self, x):\n        c = self.conv_transpose(x).contiguous()\n        N, C, D, H, W = c.shape\n        P1D, P1H, P1W = D // 2, H // 2, W // 2\n        OD, OH, OW = P1D // 3, P1H // 3, P1W // 3\n        out = torch.empty((N, 1, OD, OH, OW), device=c.device, dtype=c.dtype)\n        total = N * OD * OH * OW\n        BLOCK = 128\n        grid = (triton.cdiv(total, BLOCK),)\n        fused_kernel[grid](c, out, N, C, D, H, W, OD, OH, OW, total, BLOCK=BLOCK)\n        return out\n```", "L2_092": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier conv problems (wrong results or slower than eager)\n- Pitfall: Avoid per-element div/mod index decoding plus per-tap weight gathers in stencil kernels. Use a 2D/3D grid (plane, row-tile, col-tile) and load per-channel weights once per program.\n- Pitfall: For depthwise conv, don'...'s 2D output plane, reuse input rows via shared memory or registers, and make kernel dims constexpr.\n- Pitfall: Fuse post-conv elementwise/reduction ops with following pooling into one kernel instead of separate launches that write and re-read full-size intermediates. Unfused memory-bound epilogues after cuDNN conv easily end up slower than eager.\n- Pitfall: For softmax or reduction over the channel dim of NC... tensors, avoid one program per spatial position with channel-strided loads. Tile a 2D [channels \u00d7 contiguous spatial block] so loads coalesce along the innermost dimension.\n- Pitfall: Don't wrap the cuDNN/PyTorch op and then add a no-op copy kernel. The extra full-tensor read/write plus launch only adds time. Write a real fused kernel that replaces or eliminates work.\n\n### Verified recipes for conv problems (speedups measured by the protected evaluator)\n- [2.43x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv with a direct Triton kernel, since cuDNN's depthwise path is slow. Keep nn.Conv2d only as the parameter holder. Use a 2D grid: program 0 covers one (n, c, oh) output row, decoded with div/mod; program 1 covers a BLOCK=256 tile of contiguous ow, using num_warps=4. Unroll the kernel taps with tl.static_range. Load the scalar weight per tap and coalesced input rows with masks for padding bounds. Accumulate in fp32, fuse the optional bias via a constexpr flag, and use int64 base offsets.\n- [2.25x on conv_depthwise_2D_square_input_asymmetric_kernel] Replace cuDNN depthwise/grouped conv (slow in fp32) with a Triton direct-convolution kernel. Use one flattened 1D grid over NCHW outputs with BLOCK\u2248256. Decode n, c, oh, ow by div/mod so adjacent lanes read adjacent ow for coalesced loads. Loop over the small kernel taps, masking out-of-range input coordinates (handles padding/stride/dilation). Load the per-channel weight scalar and add bias under a constexpr flag. Accumulate in fp32 and compute base offsets in int64. Keep the nn.Conv2d module only for parameter storage.\n- [1.94x on Conv2d_Tanh_Scaling_BiasAdd_Max] Keep the convolution in cuDNN via torch (nn.Conv2d / F.conv2d, contiguous NCHW output). Fuse every following elementwise op (activation, scale, per-channel bias) with the pooling into one Triton kernel. Launch one thread per pooled output element, decoding n,c,oh,ow from a flat index. Loop over the PxP window, load, apply libdevice tanh, scale, add bias, keep a running max, then store once. Use int64 base offsets for large tensors, BLOCK=256 on a 1D grid, and keep all math in fp32.\n- [1.68x on Conv2d_BatchNorm_Scaling] Leave the conv itself to cuDNN via torch. Replace training-mode BatchNorm plus any elementwise tail with two Triton passes. Pass 1 computes per-channel sum and sum-of-squares on a 2D grid (channel, spatial block). Loop over the batch with contiguous, coalesced spatial loads, accumulate in fp32 registers, reduce, then atomic_add per channel. Do mean, var and rsqrt on tiny C-sized tensors in torch, and update running stats with unbiased var. Pass 2 is a flat 1D elementwise kernel with c=(offs//S)%C that fuses normalize, affine and scale. Use int64 offsets.\n- [1.61x on Conv2d_GroupNorm_Scale_MaxPool_Clamp] Keep the conv in cuDNN via torch (F.conv2d / nn.Conv2d). Replace GroupNorm plus the epilogue with two Triton kernels. Kernel 1: one program per (n, group) streams the group's contiguous CPG*H*W slab with BLOCK=1024 vector loads, accumulates sum and sum-of-squares in fp32, and writes mean and invstd. Kernel 2: one thread per pooled output element. Load per-channel affine and scale, normalize each window value, then max-reduce and clamp in registers before a single store. Use int64 base offsets and initialize the max with -3.4e38.\n\n### A verified kernel for a related conv problem (L2_069 Conv2d_HardSwish_ReLU, 1.25x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef act_kernel(x_ptr, out_ptr, TOTAL, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < TOTAL\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    # hardswish: x * clamp(x+3,0,6)/6\n    hs = v * tl.minimum(tl.maximum(v + 3.0, 0.0), 6.0) / 6.0\n    r = tl.maximum(hs, 0.0)\n    tl.store(out_ptr + offs, r, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        out = self.conv(x).contiguous()\n        TOTAL = out.numel()\n        res = torch.empty_like(out)\n        BLOCK = 1024\n        grid = (triton.cdiv(TOTAL, BLOCK),)\n        act_kernel[grid](out, res, TOTAL, BLOCK=BLOCK)\n        return res\n```\n\n### A verified kernel for a related conv problem (L2_025 Conv2d_Min_Tanh_Tanh, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef min_tanh_kernel(x_ptr, out_ptr, C, S, NS, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < NS\n    n = offs // S\n    s = offs % S\n    base = n.to(tl.int64) * C * S + s\n    acc = tl.full((BLOCK,), 1e30, tl.float32)\n    for c in range(C):\n        v = tl.load(x_ptr + base + c * S, mask=mask, other=1e30)\n        acc = tl.minimum(acc, v)\n    acc = tl.minimum(tl.maximum(acc, -1e30), 1e30)\n    t = tl.extra.cuda.libdevice.tanh(acc)\n    t = tl.extra.cuda.libdevice.tanh(t)\n    tl.store(out_ptr + offs, t, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size):\n        super(ModelNew, self).__init__()\n        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)\n\n    def forward(self, x):\n        x = self.conv(x).contiguous()\n        N, C, H, W = x.shape\n        S = H * W\n        out = torch.empty((N, 1, H, W), device=x.device, dtype=x.dtype)\n        NS = N * S\n        BLOCK = 1024\n        grid = (triton.cdiv(NS, BLOCK),)\n        min_tanh_kernel[grid](x, out, C, S, NS, BLOCK=BLOCK)\n        return out\n```", "L2_094": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_053 Gemm_Scaling_Hardtanh_GELU, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef epilogue_kernel(x_ptr, out_ptr, scaling, hmin, hmax, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask)\n    v = v * scaling\n    v = tl.minimum(tl.maximum(v, hmin), hmax)\n    g = 0.5 * v * (1.0 + tl.erf(v * 0.7071067811865476))\n    tl.store(out_ptr + offs, g, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, scaling_factor, hardtanh_min, hardtanh_max):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features)\n        self.scaling_factor = scaling_factor\n        self.hardtanh_min = hardtanh_min\n        self.hardtanh_max = hardtanh_max\n\n    def forward(self, x):\n        z = self.gemm(x)\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        epilogue_kernel[grid](z, out, self.scaling_factor,\n                              float(self.hardtanh_min), float(self.hardtanh_max),\n                              n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L2_029 Matmul_Mish_Mish, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef mish2_kernel(x_ptr, out_ptr, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    v = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    sp = tl.log(1.0 + tl.exp(v))\n    y = v * (tl.exp(sp) - tl.exp(-sp)) / (tl.exp(sp) + tl.exp(-sp))\n    sp2 = tl.log(1.0 + tl.exp(y))\n    z = y * (tl.exp(sp2) - tl.exp(-sp2)) / (tl.exp(sp2) + tl.exp(-sp2))\n    tl.store(out_ptr + offs, z, mask=mask)\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features):\n        super().__init__()\n        self.linear = nn.Linear(in_features, out_features)\n\n    def forward(self, x):\n        z = self.linear(x).contiguous()\n        out = torch.empty_like(z)\n        n = z.numel()\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        mish2_kernel[grid](z, out, n, BLOCK=BLOCK)\n        return out\n```", "L3_004": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_008": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_009": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_010": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_014": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_020": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_021": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_023": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_024": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier network problems (wrong results or slower than eager)\n- Pitfall: For per-channel affine ops on NCHW, launch a 2D grid (one program per N*C row, tiles over HW). Precompute per-channel scale/shift once, instead of per-element div/mod, four parameter gathers and an rsqrt.\n- Pitfall: Don't replace cuDNN BatchNorm in training mode with separate torch mean/var reductions, running-stat updates and an elementwise kernel. The extra launches and memory passes outweigh the fusion; it ran far slower than eager.\n- Pitfall: Do not cache derived weights or folded parameters on the first forward call. Recompute them from the live parameters, or confirm that both modes match the reference within 1e-4.\n- Pitfall: Do not fold BatchNorm into conv weights using running_mean/var. The evaluator may run the reference in training mode, where BN normalizes with batch statistics. Check self.training, or compute batch stats yourself.\n\n### Verified recipes for network problems (speedups measured by the protected evaluator)\n- [1.00x on RegNet] Keep convolutions, pooling and Linear in cuDNN/cuBLAS via torch. Fuse BatchNorm+ReLU into one elementwise Triton kernel. Precompute per-channel scale=w/sqrt(var+eps) and shift=b-mean*scale in torch. In training mode use batch mean/var (unbiased=False) and update running stats with the unbiased correction n/(n-1). Index channels with (offs//HW)%C on contiguous NCHW, use 1D BLOCK=1024 with masking, and do fp32 math throughout. Gains are small (~1.005x). For more, fuse BN+ReLU+maxpool or the final pool with GAP.\n\n### A verified kernel for a related network problem (L3_027 RegNet, 1.00x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef bn_relu_kernel(x_ptr, out_ptr, scale_ptr, shift_ptr, HW, C, n_elem, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n_elem\n    c = (offs // HW) % C\n    x = tl.load(x_ptr + offs, mask=mask, other=0.0)\n    s = tl.load(scale_ptr + c, mask=mask, other=0.0)\n    sh = tl.load(shift_ptr + c, mask=mask, other=0.0)\n    y = x * s + sh\n    y = tl.maximum(y, 0.0)\n    tl.store(out_ptr + offs, y, mask=mask)\n\ndef apply_bn_relu(x, scale, shift):\n    N, C, H, W = x.shape\n    out = torch.empty_like(x)\n    HW = H * W\n    n = x.numel()\n    grid = (triton.cdiv(n, 1024),)\n    bn_relu_kernel[grid](x, out, scale.contiguous(), shift.contiguous(), HW, C, n, BLOCK=1024)\n    return out\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_channels, stages, block_widths, output_classes):\n        super(ModelNew, self).__init__()\n        self.stages = stages\n        self.block_widths = block_widths\n        layers = []\n        current = input_channels\n        for i in range(stages):\n            layers.append(nn.Sequential(\n                nn.Conv2d(current, block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.Conv2d(block_widths[i], block_widths[i], kernel_size=3, padding=1),\n                nn.BatchNorm2d(block_widths[i]),\n                nn.ReLU(),\n                nn.MaxPool2d(kernel_size=2, stride=2),\n            ))\n            current = block_widths[i]\n        self.feature_extractor = nn.Sequential(*layers)\n        self.fc = nn.Linear(block_widths[-1], output_classes)\n\n    def _bn_params(self, bn, x):\n        if self.training:\n            mean = x.mean(dim=[0, 2, 3])\n            var = x.var(dim=[0, 2, 3], unbiased=False)\n            n = x.numel() // x.shape[1]\n            with torch.no_grad():\n                bn.running_mean.mul_(1 - bn.momentum).add_(bn.momentum * mean)\n                bn.running_var.mul_(1 - bn.momentum).add_(bn.momentum * var * n / (n - 1))\n        else:\n            mean = bn.running_mean\n            var = bn.running_var\n        scale = bn.weight / torch.sqrt(var + bn.eps)\n        shift = bn.bias - mean * scale\n        return scale, shift\n\n    def forward(self, x):\n        for stage in self.feature_extractor:\n            conv1 = stage[0]\n            bn1 = stage[1]\n            conv2 = stage[3]\n            bn2 = stage[4]\n            pool = stage[6]\n            x = conv1(x)\n            s, sh = self._bn_params(bn1, x)\n            x = apply_bn_relu(x, s, sh)\n            x = conv2(x)\n            s, sh = self._bn_params(bn2, x)\n            x = apply_bn_relu(x, s, sh)\n            x = pool(x)\n        x = torch.mean(x, dim=[2, 3])\n        x = self.fc(x)\n        return x\n```", "L3_030": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_032": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing.", "L3_036": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_037": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_038": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_039": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_040": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_041": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_042": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier rnn problems (wrong results or slower than eager)\n- Pitfall: Before writing a kernel, check whether the eager baseline is already one fused vendor-library call (cuDNN RNN, cuBLAS). Decomposing it into many smaller launches is almost always slower, even when correct.\n- Pitfall: For recurrent ops, don't replace cuDNN with a Python per-timestep loop launching separate GEMM and gate kernels. Launch overhead dominates and yields big slowdowns, so keep cuDNN or fuse the entire time loop into one persistent kernel.\n- Pitfall: Gains must come from fusing or eliminating real work, such as skipping computations whose results are never returned. A trivial copy or pass-through kernel cannot beat eager.\n- Pitfall: Don't call the cuDNN/PyTorch op and then append a token Triton copy kernel. The extra launch and allocation only make it slower than eager. Return library outputs directly, or replace real work with fused kernels.\n- Pitfall: Avoid one-program-per-output-element dot-product kernels (tl.sum per element) for matmuls; use tiled tl.dot or keep cuBLAS, since naive reductions lose to eager even at small sizes.\n- Pitfall: Don't wrap the dominant op (e.g., cuDNN LSTM) in PyTorch and only replace a tiny trailing linear with a custom kernel. Launch overhead plus a naive dot-product kernel makes it slower; optimize the actual hot path.\n\n### Verified recipes for rnn problems (speedups measured by the protected evaluator)\n- [1.03x on VanillaRNN] Keep every GEMM in cuBLAS through torch (matmul/addmm, F.linear). Drop torch.cat in a concat-then-Linear cell: slice the weight into W_x and W_h column views, compute x@W_x.T, then accumulate h@W_h.T in place with addmm_. Fuse bias-add and tanh into a single Triton elementwise pass, one program per row, looping over columns in 1024-wide masked blocks. Accumulate in fp32 and use an exact tanh formula. Expect only small gains because the large GEMMs dominate runtime.\n\n### A verified kernel for a related rnn problem (L3_033 VanillaRNN, 1.03x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\nbatch_size = 256\ninput_size = 16384\nhidden_size = 16384\noutput_size = 8192\n\n@triton.jit\ndef bias_tanh_kernel(x_ptr, b_ptr, out_ptr, n_rows, n_cols, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    row = pid\n    offs = tl.arange(0, BLOCK)\n    for c in range(0, n_cols, BLOCK):\n        idx = c + offs\n        mask = idx < n_cols\n        v = tl.load(x_ptr + row * n_cols + idx, mask=mask, other=0.0)\n        b = tl.load(b_ptr + idx, mask=mask, other=0.0)\n        r = v + b\n        r = (tl.exp(2.0 * r) - 1.0) / (tl.exp(2.0 * r) + 1.0)\n        tl.store(out_ptr + row * n_cols + idx, r, mask=mask)\n\n\ndef bias_tanh(x, b):\n    n_rows, n_cols = x.shape\n    out = torch.empty_like(x)\n    grid = (n_rows,)\n    bias_tanh_kernel[grid](x, b, out, n_rows, n_cols, BLOCK=1024)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n        self.hidden = torch.randn((batch_size, hidden_size))\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, initial_hidden=None) -> torch.Tensor:\n        if initial_hidden is not None:\n            self.hidden.copy_(initial_hidden)\n        self.hidden = self.hidden.to(x.device)\n\n        W = self.i2h.weight  # (hidden, input+hidden)\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n\n        # pre-activation = x @ W_x.T + hidden @ W_h.T + bias\n        pre = x @ W_x.t()\n        pre = pre.addmm_(self.hidden, W_h.t())\n\n        new_hidden = bias_tanh(pre, self.i2h.bias)\n        self.hidden = new_hidden\n\n        output = self.h2o(new_hidden)\n        return output\n```\n\n### A verified kernel for a related rnn problem (L3_034 VanillaRNNHidden, 1.01x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef bias_tanh_kernel(pre_ptr, b_ptr, out_ptr, n_rows, hidden_size, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = tl.arange(0, BLOCK)\n    mask = offs < hidden_size\n    v = tl.load(pre_ptr + pid * hidden_size + offs, mask=mask, other=0.0)\n    b = tl.load(b_ptr + offs, mask=mask, other=0.0)\n    r = v + b\n    e = tl.exp(2.0 * r)\n    r = (e - 1.0) / (e + 1.0)\n    tl.store(out_ptr + pid * hidden_size + offs, r, mask=mask)\n\n\ndef bias_tanh(pre, b, out):\n    n_rows, hidden_size = pre.shape\n    BLOCK = triton.next_power_of_2(hidden_size)\n    bias_tanh_kernel[(n_rows,)](pre, b, out, n_rows, hidden_size, BLOCK=BLOCK)\n    return out\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, input_size: int, hidden_size: int, output_size: int):\n        super(ModelNew, self).__init__()\n        self.input_size = input_size\n        self.hidden_size = hidden_size\n        self.output_size = output_size\n\n        self.i2h = nn.Linear(input_size + hidden_size, hidden_size)\n        self.h2o = nn.Linear(hidden_size, output_size)\n        self.tanh = nn.Tanh()\n\n    def forward(self, x: torch.Tensor, h0: torch.Tensor) -> torch.Tensor:\n        seq_len, batch_size, _ = x.size()\n        hidden = h0.to(x.device)\n\n        W = self.i2h.weight\n        W_x = W[:, :self.input_size]\n        W_h = W[:, self.input_size:]\n        b = self.i2h.bias\n\n        x2d = x.reshape(seq_len * batch_size, self.input_size)\n        pre_all = (x2d @ W_x.t()).reshape(seq_len, batch_size, self.hidden_size)\n\n        Wh_t = W_h.t().contiguous()\n\n        hiddens = torch.empty(seq_len, batch_size, self.hidden_size,\n                              device=x.device, dtype=x.dtype)\n\n        for t in range(seq_len):\n            pre = pre_all[t].addmm(hidden, Wh_t)\n            hidden = bias_tanh(pre, b, hiddens[t])\n\n        h2d = hiddens.reshape(seq_len * batch_size, self.hidden_size)\n        out = self.h2o(h2d).reshape(seq_len, batch_size, self.output_size)\n        return out\n```", "L3_046": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier matmul problems (wrong results or slower than eager)\n- Pitfall: When using split-K, keep the split count small; a very large split writes and re-reads a huge partial-sum buffer plus an extra reduction launch, eating the occupancy gain.\n- Pitfall: Strict fp32 Triton tl.dot (allow_tf32=False) rarely beats cuBLAS on matmul; a hand split-K version was correct but still 0.88x. Fuse surrounding ops or exploit structure instead of reimplementing plain GEMM.\n- Pitfall: For bandwidth-bound Triton kernels, give each program more work: larger tiles, multiple rows per program, more warps. Tiny per-program work and Python launch overhead lose to cuBLAS/ATen kernels.\n- Pitfall: Don't expect a single-pass memory-bound elementwise or broadcast kernel to beat eager, which already runs near bandwidth peak. Win by fusing multiple ops or reducing memory traffic.\n- Pitfall: If writing a Triton GEMM anyway, use @triton.autotune over several BM/BN/BK, num_warps and num_stages configs, plus grouped tile ordering. A single fixed 64x64x32 config is far slower than eager.\n- Pitfall: Do not hand-write a plain fp32 matmul with TF32 disabled; it loses to cuBLAS. Call torch.matmul on transposed views (no .contiguous copies) and spend custom-kernel effort only on fusing surrounding ops.\n\n### Verified recipes for matmul problems (speedups measured by the protected evaluator)\n- [36.02x on Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd] Look for algebraic collapse before writing kernels. When a GEMM feeds a linear reduction (a mean or sum over output features), rewrite mean(Wx+b-s) as x\u00b7(W.sum(0)/N) + mean(b-s). This turns the GEMM into a GEMV kept in torch/cuBLAS. Check for degenerate ops: logsumexp over a size-1 dim is the identity, so drop it. Apply cheap scalar ops such as GELU on the reduced vector in torch. Fuse the final per-row broadcast plus residual add into one coalesced 1D Triton elementwise kernel (BLOCK=1024, row = offs // n_feat). fp32 summation stays within 1e-4.\n- [4.58x on Matmul_for_lower_triangular_matrices] Exploit structural sparsity (triangular, banded, diagonal) with a custom Triton tiled matmul instead of dense cuBLAS. Use a 2D grid of output tiles and return early for tiles that are entirely zero. Clamp the K-loop to the nonzero range: for tril\u00d7tril, run from floor(n_lo/BK)*BK to min(m_lo+BM, N). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the output mask with tl.where before the store. Pre-zero the output with torch.zeros so skipped tiles stay zero. 64x64x32 tiles, 4 warps, 3 stages.\n- [4.11x on Matmul_for_upper_triangular_matrices] Exploit structural sparsity (triangular, banded, or block-sparse) with a Triton tiled GEMM instead of dense cuBLAS. Use a 2D grid over output tiles, early-return tiles that are entirely masked out, and clip the K loop to the nonzero range (for triu\u00b7triu, k from the row-tile start to the column-tile end, aligned to BLOCK_K). Accumulate in fp32 with tl.dot(allow_tf32=False) to stay within 1e-4. Apply the triangle mask with tl.where before storing. Preallocate the output with torch.zeros so skipped tiles stay zero. Tiles 64x64x32, 4 warps, 3 stages.\n- [1.02x on Matmul_BatchNorm_BiasAdd_Divide_Swish] Keep the GEMM (nn.Linear) in cuBLAS via torch and fuse only the epilogue in Triton. For training-mode BatchNorm, run a per-column stats kernel that accumulates sum and sum-of-squares in fp32, giving biased variance for normalization. Update running_mean/var under no_grad using the unbiased var, M/(M-1). Then one flat elementwise kernel applies normalize, gamma/beta, bias, divide and Swish, indexing per-column params with offs % N. Gains are small because the GEMM dominates; next, coalesce stats loads with 2D column tiles.\n- [1.01x on Matmul_GroupNorm_LeakyReLU_Sum] Keep the Linear GEMM in cuBLAS via the module's own fc (F.linear with bias). Fuse every downstream per-row op into one Triton kernel reading the GEMM output once: GroupNorm, affine, LeakyReLU and x+x (as y*2). Use one program per (row, group), BLOCK=next_power_of_2(group size), contiguous masked loads. Compute the two-pass mean/variance in fp32 registers and mask padded lanes before squaring. Expect small gains, since the GEMM dominates; for tiny groups, batch several groups per program to cut launch and occupancy waste.\n- [1.01x on Gemm_Sigmoid_Scaling_ResidualAdd] Keep the GEMM in cuBLAS through nn.Linear / F.linear in fp32, with the bias folded in by cuBLAS. Replace the chain of eager elementwise ops (sigmoid, scale, residual add) with a single flat 1D Triton kernel: one load, compute s=1/(1+exp(-v)), y=s*scale+v, one store. Use contiguous masked blocks of 1024 and grid=cdiv(n,BLOCK). Writing in place into the GEMM output saves an allocation. The gain is small because the GEMM dominates; a bigger win requires a fused-epilogue GEMM.\n\n### A verified kernel for a related matmul problem (L2_051 Gemm_Subtract_GlobalAvgPool_LogSumExp_GELU_ResidualAdd, 36.02x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(x_ptr, s_ptr, out_ptr, n_feat, n, BLOCK: tl.constexpr):\n    pid = tl.program_id(0)\n    offs = pid * BLOCK + tl.arange(0, BLOCK)\n    mask = offs < n\n    row = offs // n_feat\n    v = tl.load(x_ptr + offs, mask=mask)\n    s = tl.load(s_ptr + row, mask=mask)\n    tl.store(out_ptr + offs, v + s, mask=mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self, in_features, out_features, bias=True):\n        super().__init__()\n        self.gemm = nn.Linear(in_features, out_features, bias=bias)\n        self.subtract = nn.Parameter(torch.randn(out_features))\n        self.out_features = out_features\n\n    def forward(self, x):\n        # mean over output features of (Wx + b - subtract) = (colsum/out)\u00b7x + c\n        colsum = self.gemm.weight.sum(dim=0) / self.out_features  # (in,)\n        if self.gemm.bias is not None:\n            c = (self.gemm.bias - self.subtract).mean()\n        else:\n            c = (-self.subtract).mean()\n        s = x @ colsum + c  # (batch,)\n        # logsumexp over single element (dim=1 after keepdim mean) is identity\n        s = F.gelu(s)\n        out = torch.empty_like(x)\n        n = x.numel()\n        n_feat = x.shape[1]\n        BLOCK = 1024\n        grid = (triton.cdiv(n, BLOCK),)\n        add_kernel[grid](x, s, out, n_feat, n, BLOCK=BLOCK)\n        return out\n```\n\n### A verified kernel for a related matmul problem (L1_015 Matmul_for_lower_triangular_matrices, 4.58x): adapt what applies\n```python\nimport torch\nimport torch.nn as nn\nimport triton\nimport triton.language as tl\n\n@triton.jit\ndef tril_mm_kernel(A_ptr, B_ptr, C_ptr, N,\n                   BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr):\n    pid_m = tl.program_id(0)\n    pid_n = tl.program_id(1)\n\n    m_lo = pid_m * BLOCK_M\n    n_lo = pid_n * BLOCK_N\n\n    if n_lo > (m_lo + BLOCK_M - 1):\n        return\n\n    offs_m = m_lo + tl.arange(0, BLOCK_M)\n    offs_n = n_lo + tl.arange(0, BLOCK_N)\n    offs_k = tl.arange(0, BLOCK_K)\n\n    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)\n\n    k_start = (n_lo // BLOCK_K) * BLOCK_K\n    k_end = tl.minimum(m_lo + BLOCK_M, N)\n\n    k = k_start\n    while k < k_end:\n        kk = k + offs_k\n        a = tl.load(A_ptr + offs_m[:, None] * N + kk[None, :],\n                    mask=(offs_m[:, None] < N) & (kk[None, :] < N), other=0.0)\n        b = tl.load(B_ptr + kk[:, None] * N + offs_n[None, :],\n                    mask=(kk[:, None] < N) & (offs_n[None, :] < N), other=0.0)\n        acc += tl.dot(a, b, allow_tf32=False)\n        k += BLOCK_K\n\n    mask_tri = offs_m[:, None] >= offs_n[None, :]\n    acc = tl.where(mask_tri, acc, 0.0)\n    store_mask = (offs_m[:, None] < N) & (offs_n[None, :] < N)\n    tl.store(C_ptr + offs_m[:, None] * N + offs_n[None, :], acc, mask=store_mask)\n\n\nclass ModelNew(nn.Module):\n    def __init__(self):\n        super().__init__()\n\n    def forward(self, A, B):\n        A = A.contiguous()\n        B = B.contiguous()\n        N = A.shape[0]\n        C = torch.zeros_like(A)\n        BLOCK_M = 64\n        BLOCK_N = 64\n        BLOCK_K = 32\n        grid = (triton.cdiv(N, BLOCK_M), triton.cdiv(N, BLOCK_N))\n        tril_mm_kernel[grid](A, B, C, N, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_K=BLOCK_K,\n                             num_warps=4, num_stages=3)\n        return C\n```", "L3_049": "## Kernel memory (items verified by the protected evaluator on training problems; may not all apply)\n\n### Lessons about this environment (from official checker verdicts and verified outcomes)\n- Checker rule: getattr needs a literal, non-private attribute name\n- Pitfall: A reply without a ```python fenced code block was rejected by the checker. Always wrap the full ModelNew source in a ```python block.\n- Pitfall: Output mismatch beyond 1e-4 occurred repeatedly. Fix by forcing exact fp32 tl.dot(allow_tf32=False) and exact masking: K bounds at block granularity, tril mask, and zero-initialized output for skipped tiles.\n- Checker rule: forward modified its input tensors in place\n- Checker rule: do not define a class named Model (the reference); define ModelNew only\n- Process: never SUBMIT code that has not passed ACTION: CHECK in this episode. Untested submissions that fail to compile or mismatch the reference score 0; a CHECK costs one reply and shows the compiler output.\n- Pitfall: cpp_sources is compiled by plain c++ without CUDA headers: never use cudaStream_t or at::cuda::getCurrentCUDAStream there. Put wrappers needing streams in cuda_sources, keeping only plain-type prototypes in cpp_sources.\n- Pitfall: If cpp_sources must reference CUDA types or the current stream, explicitly #include <cuda_runtime.h> and <ATen/cuda/CUDAContext.h>; torch/extension.h does not provide them.\n- Checker rule: assignment to attribute 'm.conv1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn1' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.conv2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.bn2' is not allowed (only self.<x>)\n- Checker rule: assignment to attribute 'm.downsample' is not allowed (only self.<x>)\n- Checker rule: At least one of your own kernels must actually launch during forward; a pure torch path (even with a compiled but unused kernel) is rejected as no_custom_kernel.\n\n### Pitfalls seen on earlier attention problems (wrong results or slower than eager)\n- Pitfall: Handle every optional forward argument (e.g. initial_states) and every intermediate the reference includes, even when it defaults to zeros. Verify the returned tensor is the same slice and quantity the reference returns.\n- Pitfall: Do not algebraically restructure the reference'...'s exact operation order and test against it before optimizing."}}}